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This article is cited in 43 scientific papers (total in 43 papers)
Explicit form of the law of reciprocity
S. V. Vostokov
Abstract:
A pairing in the multiplicative group of a local field (a finite extension of a $p$-adic number field) is defined in terms of the expansion of elements into series in a local uniformizing parameter. The main properties of this pairing are proved: bilinearity, skew-symmetry, invariance with respect to choice of local uniformizing parameter, and independence of the choice of expansion of elements into series in this uniformizing parameter. In addition, the norm property of this pairing is examined. The main result of this paper is that this pairing coincides with Hilbert's norm residue symbol. This yields an explicit formula for the latter.
Bibliography: 9 titles.
Received: 06.06.1978
Citation:
S. V. Vostokov, “Explicit form of the law of reciprocity”, Izv. Akad. Nauk SSSR Ser. Mat., 42:6 (1978), 1288–1321; Math. USSR-Izv., 13:3 (1979), 557–588
Linking options:
https://www.mathnet.ru/eng/im1967https://doi.org/10.1070/IM1979v013n03ABEH002077 https://www.mathnet.ru/eng/im/v42/i6/p1288
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Abstract page: | 1112 | Russian version PDF: | 419 | English version PDF: | 21 | References: | 67 | First page: | 1 |
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